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- Pure_type_system abstract "In the branches of mathematical logic known as proof theory and type theory, a pure type system (PTS), previously known as a generalized type system (GTS), is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these. The framework can be seen as a generalisation of Barendregt's lambda cube, in the sense that all corners of the cube can be represented as instances of a PTS with just two sorts. In fact Barendregt (1991) framed his cube in this setting. Pure type systems may obscure the distinction between types and terms and collapse the type hierarchy, as is the case with the calculus of constructions, but this is not generally the case, e.g. the simply typed lambda calculus allows only terms to depend on types.Pure type systems were independently introduced by Stefano Berardi (1988) and Jan Terlouw (1989). Barendregt discussed them at length in his subsequent papers. In his PhD thesis, Berardi defined a cube of constructive logics akin to the lambda cube (these specifications are non-dependent). A modification of this cube was later called the L-cube by Geuvers, who in his PhD thesis extended the Curry–Howard correspondence to this setting. Based on these ideas, Barthe and others defined classical pure type systems (CPTS) by adding a double negation operator. \tSimilarly, in 1998, Tijn Borghuis introduced modal pure type systems (MPTS). Roorda has discussed the application of pure type systems to functional programming; and Roorda and Jeuring have proposed a programming language based on pure type systems.The systems from the lambda cube are all known to be strongly normalizing. Pure type systems in general need not be, for example System U from Girard's paradox is not. (Roughly speaking, Girard found pure systems in which one can express the sentence \"the types form a type\".) Furthermore, all known examples of pure type systems that are not strongly normalizing are not even (weakly) normalizing: they contain expressions that do not have normal forms, just like the untyped lambda calculus. It is a major open problem in the field whether this is always the case, i.e. whether a (weakly) normalizing PTS always has the strong normalization property. This is known as the Barendregt–Geuvers–Klop conjecture (named after Henk Barendregt, Herman Geuvers, and Jan Willem Klop).".
- Pure_type_system wikiPageExternalLink jwroorda.
- Pure_type_system wikiPageExternalLink sage.soe.ucsc.edu.
- Pure_type_system wikiPageExternalLink yarrow.
- Pure_type_system wikiPageExternalLink tlc004.htm.
- Pure_type_system wikiPageID "17870536".
- Pure_type_system wikiPageLength "6760".
- Pure_type_system wikiPageOutDegree "24".
- Pure_type_system wikiPageRevisionID "705764109".
- Pure_type_system wikiPageWikiLink Calculus_of_constructions.
- Pure_type_system wikiPageWikiLink Category:Lambda_calculus.
- Pure_type_system wikiPageWikiLink Category:Proof_theory.
- Pure_type_system wikiPageWikiLink Category:Type_theory.
- Pure_type_system wikiPageWikiLink Curry–Howard_correspondence.
- Pure_type_system wikiPageWikiLink Double_negation.
- Pure_type_system wikiPageWikiLink Henk_Barendregt.
- Pure_type_system wikiPageWikiLink Intuitionistic_logic.
- Pure_type_system wikiPageWikiLink Jan_Willem_Klop.
- Pure_type_system wikiPageWikiLink Jean-Yves_Girard.
- Pure_type_system wikiPageWikiLink Lambda-mu_calculus.
- Pure_type_system wikiPageWikiLink Lambda_cube.
- Pure_type_system wikiPageWikiLink Mathematical_logic.
- Pure_type_system wikiPageWikiLink Normal_form_(abstract_rewriting).
- Pure_type_system wikiPageWikiLink Normalization_property_(abstract_rewriting).
- Pure_type_system wikiPageWikiLink Proof_theory.
- Pure_type_system wikiPageWikiLink Simply_typed_lambda_calculus.
- Pure_type_system wikiPageWikiLink Structure_(mathematical_logic).
- Pure_type_system wikiPageWikiLink System_U.
- Pure_type_system wikiPageWikiLink Type_hierarchy.
- Pure_type_system wikiPageWikiLink Type_theory.
- Pure_type_system wikiPageWikiLink Typed_lambda_calculus.
- Pure_type_system wikiPageWikiLinkText "Girard's Paradox".
- Pure_type_system wikiPageWikiLinkText "Pure type system".
- Pure_type_system wikiPageWikiLinkText "pure type system".
- Pure_type_system id "pure+type+system".
- Pure_type_system title "Pure type system".
- Pure_type_system wikiPageUsesTemplate Template:Citation_needed.
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- Pure_type_system wikiPageUsesTemplate Template:Refend.
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- Pure_type_system subject Category:Lambda_calculus.
- Pure_type_system subject Category:Proof_theory.
- Pure_type_system subject Category:Type_theory.
- Pure_type_system hypernym Form.
- Pure_type_system type Model.
- Pure_type_system type Model.
- Pure_type_system type Proof.
- Pure_type_system type Redirect.
- Pure_type_system comment "In the branches of mathematical logic known as proof theory and type theory, a pure type system (PTS), previously known as a generalized type system (GTS), is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these. The framework can be seen as a generalisation of Barendregt's lambda cube, in the sense that all corners of the cube can be represented as instances of a PTS with just two sorts.".
- Pure_type_system label "Pure type system".
- Pure_type_system sameAs Q7261163.
- Pure_type_system sameAs Αμιγές_σύστημα_τύπων.
- Pure_type_system sameAs m.047d_b3.
- Pure_type_system sameAs Q7261163.
- Pure_type_system wasDerivedFrom Pure_type_system?oldid=705764109.
- Pure_type_system isPrimaryTopicOf Pure_type_system.